$J$ $K$ $L$ If: $ JK = 6x + 6$, $ KL = 7x + 7$, and $ JL = 52$, Find $KL$.
Solution: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {6x + 6} + {7x + 7} = {52}$ Combine like terms: $ 13x + 13 = {52}$ Subtract $13$ from both sides: $ 13x = 39$ Divide both sides by $13$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $KL$ $ KL = 7({3}) + 7$ Simplify: $ {KL = 21 + 7}$ Simplify to find ${KL}$ : $ {KL = 28}$